Standard errors for reliability coefficients

Reliability analysis is one of the most conducted analyses in applied psychometrics. It entails the assessment of reliability of both item scores and scale scores using coefficients that estimate the reliability (e.g. Cronbach's alpha), estimate measurement precision (e.g., estimated standard error of measurement), or estimate the contribution of individual items to the reliability (e.g., corrected item-total correlations). Most statistical software packages used in the social and behavioral sciences offer these reliability coefficients whereas standard errors are generally unavailable, which is a bit ironic for coefficients about measurement precision. This paper provides analytic large-sample standard errors for coefficients used in reliability analysis. As most scores used in the behavioral sciences are discrete, the standard errors were derived under the relatively unrestrictive multinomial sampling scheme. The tedious derivations have been diverted to appendices, and R functions for computing the standard errors are available from the Open Science Framework. Bias and variance of the standard errors, and coverage of the corresponding Wald-based confidence intervals were studied using simulated item scores. Bias and variance, and coverage were generally satisfactory for larger sample sizes, and parameter values not close to the boundary of the parameter space.